Finite Group Databasebeta

← C3×#24148 #10642755

Subgroups — C3×#24148 #10642755

Order 768.

1102 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3510C211yesmaximal, characteristic, complemented
2C3×#3077C211yesmaximal, characteristic, complemented
3C3×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C3×#2544C211yesmaximal, characteristic, complemented
5C3×#2038C211yesmaximal, characteristic, complemented
6C3×#2037C211yesmaximal, characteristic, complemented
7C3×#2003C211yesmaximal, characteristic, complemented
8C3×#2002C211yesmaximal, characteristic
9C3×#1986C211yesmaximal, characteristic, complemented
10C3×#1967C211yesmaximal, characteristic, complemented
11C3×#1888C211yesmaximal, characteristic, complemented
12C3×#1887C211yesmaximal, characteristic, complemented
13C3×#1857C211yesmaximal, characteristic, complemented
14C3×#1856C211yesmaximal, characteristic, complemented
15C3×#1806C211yesmaximal, characteristic, complemented
16#24148C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
18C3×#559—21no—
19C3×#559—21no—
20C3×#556—21no—
21C3×#556—21no—
22C3×#551—22no—
23C3×#551—22no—
24C3×#542—21no—
25C3×#542—21no—
26C3×#536C2211yescharacteristic
27C3×#535C2211yescharacteristic
28C3×#533C2211yescharacteristic
29C2×C3×#127C2211yescharacteristic
30C3×#529—21no—
31C3×#529—21no—
32C2×C3×#124C2211yescharacteristic
33C2×C3×#124C2211yescharacteristic
34C3×#519C2211yescharacteristic
35C3×#518C2211yescharacteristic
36C3×C4×#41C2211yescharacteristic
37C2×C3×C4×D4C2211yescharacteristic
38C3×#478—21no—
39C3×#478—21no—
40C3×#476—21no—
41C3×#474—21no—
42C3×#442—21no—
43C3×#440—21no—
44C3×C4×SD16—21no—
45C3×C4×D8—21no—
46C3×#428C2211yescharacteristic
47C3×#428C2211yescharacteristic
48C3×#428C2211yescharacteristic
49C3×#423C2211yescharacteristic
50C2×C3×#104C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C3×#418C2211yescharacteristic
53C3×#418C2211yescharacteristic
54C3×#418C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C2×C3×#101C2211yescharacteristic
57C2×C3×#101C2211yescharacteristic
58C2×C3×#100C2211yescharacteristic
59C2×C3×#100C2211yescharacteristic
60C3×C4×M16C2211yescharacteristic
61C3×#394—22no—
62C3×#391C2211yescharacteristic
63C3×#390C2211yescharacteristic
64C3×#386—22no—
65C3×C4×C4⋊C4C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3510C2×C311yescharacteristic, complemented
73#3077C2×C311yescharacteristic, complemented
74C4×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
75#2544C2×C311yescharacteristic, complemented
76#2038C2×C311yescharacteristic, complemented
77#2037C2×C311yescharacteristic, complemented
78#2003C2×C311yescharacteristic, complemented
79#2002C2×C311yescharacteristic
80#1986C2×C311yescharacteristic, complemented
81#1967C2×C311yescharacteristic, complemented
82#1888C2×C311yescharacteristic, complemented
83#1887C2×C311yescharacteristic, complemented
84#1857C2×C311yescharacteristic, complemented
85#1856C2×C311yescharacteristic, complemented
86#1806C2×C311yescharacteristic, complemented
87C2×C3×#41C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—22no—
90C22×C3×D4C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C3×AGL(1,ℤ/8)—22no—
94C3×AGL(1,ℤ/8)—22no—
95C2×C3×SD16—21no—
96C2×C3×D8—21no—
97C2×C3×M16C2311yescharacteristic
98C2×C3×M16C2311yescharacteristic
99C2×C3×M16C2311yescharacteristic
100C2×C3×M16C2311yescharacteristic
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8D411yescharacteristic, complemented
103C3×C4⋊Q8D411yescharacteristic, complemented
104C3×#127—21no—
105C3×#127—22no—
106C3×#127—41no—
107C3×#126—22no—
108C3×#126—22no—
109C3×#126—22no—
110C3×#126—22no—
111C3×#125D411yescharacteristic, complemented
112C3×#125D411yescharacteristic, complemented
113C3×#124—22no—
114C3×#124—22no—
115C3×#124—21no—
116C3×#124—21no—
117C3×#124—22no—
118C3×#124—21no—
119C3×#124—21no—
120C3×#124—21no—
121C3×#124—21no—
122C3×#124—41no—
123C3×#123—22no—
124C3×#123—22no—
125C3×#123—22no—
126C3×#123—22no—
127C3×#123—22no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8—21no—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×#121—21no—
135C3×#121—21no—
136C3×#120—22no—
137C3×C4×Q8—21no—
138C3×C4×Q8—21no—
139C3×C4×Q8—21no—
140C3×C4×Q8—21no—
141C3×C4×Q8—21no—
142C3×C4×Q8—21no—
143C3×C4×Q8D411yescharacteristic, complemented
144C3×C4×Q8D411yescharacteristic, complemented
145C3×C4×D4—22no—
146C3×C4×D4—22no—
147C3×C4×D4—21no—
148C3×C4×D4—21no—
149C3×C4×D4—21no—
150C3×C4×D4—21no—
151C3×C4×D4—21no—
152C3×C4×D4—21no—
153C3×C4×D4—21no—
154C3×C4×D4—21no—
155C3×C4×D4—21no—
156C3×C4×D4—21no—
157C3×C4×D4D411yescharacteristic, complemented
158C3×C4×D4D411yescharacteristic, complemented
159C3×#117—22no—
160C3×#117—22no—
161C3×#117—22no—
162C3×#117—21no—
163C3×#117C2311yescharacteristic
164C3×#117C2311yescharacteristic
165C3×#117C2311yescharacteristic
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4C2311yescharacteristic
168C2×C3×C22⋊C4—22no—
169C2×C3×C22⋊C4—22no—
170C2×C3×C22⋊C4—21no—
171C2×C3×C22⋊C4—22no—
172C2×C3×C22⋊C4D412yes—
173C2×C3×C22⋊C4D412yes—
174C2×C3×C42—21no—
175C2×C3×C42C2311yescharacteristic
176C2×C3×C42C2311yescharacteristic
177C2×C3×C42C2311yescharacteristic
178C3×#107—21no—
179C3×#107—21no—
180C3×#107—21no—
181C3×#106—21no—
182C3×#106—21no—
183C3×#106—21no—
184C3×C4⋊C8—21no—
185C3×C4⋊C8—21no—
186C3×#104—41no—
187C3×#104—41no—
188C3×#103—21no—
189C3×#102—21no—
190C3×#102—21no—
191C3×#102—21no—
192C3×#102—21no—
193C3×#102—21no—
194C3×#102—21no—
195C3×#102—21no—
196C3×#101—22no—
197C3×#101—41no—
198C3×#100—22no—
199C3×#100—41no—
200C3×#97—21no—
201C3×C4×C8—21no—
202C3×#95—21no—
203C3×#95—22no—
204C2×AGL(1,ℤ/8)C22×C311yescharacteristic
205#559—21no—
206#559—21no—
207#556—21no—
208#556—21no—
209#551—22no—
210#551—22no—
211#542—21no—
212#542—21no—
213#536C22×C311yescharacteristic
214#535C22×C311yescharacteristic
215#533C22×C311yescharacteristic
216C2×#127C22×C311yescharacteristic
217#529—21no—
218#529—21no—
219C2×#124C22×C311yescharacteristic
220C2×#124C22×C311yescharacteristic
221#519C22×C311yescharacteristic
222#518C22×C311yescharacteristic
223C4×#41C22×C311yescharacteristic
224C2×C4×D4C22×C311yescharacteristic
225#478—21no—
226#478—21no—
227#476—21no—
228#474—21no—
229#442—21no—
230#440—21no—
231C4×SD16—21no—
232C4×D8—21no—
233#428C22×C311yescharacteristic
234#428C22×C311yescharacteristic
235#428C22×C311yescharacteristic
236#423C22×C311yescharacteristic
237C2×#104C22×C311yescharacteristic
238C2×#104C22×C311yescharacteristic
239#418C22×C311yescharacteristic
240#418C22×C311yescharacteristic
241#418C22×C311yescharacteristic
242#417C22×C311yescharacteristic
243C2×#101C22×C311yescharacteristic
244C2×#101C22×C311yescharacteristic
245C2×#100C22×C311yescharacteristic
246C2×#100C22×C311yescharacteristic
247C4×M16C22×C311yescharacteristic
248#394—22no—
249#391C22×C311yescharacteristic
250#390C22×C311yescharacteristic
251#386—22no—
252C4×C4⋊C4C22×C311yescharacteristic
253#339C22×C311yescharacteristic
254#339C22×C311yescharacteristic
255#339C22×C311yescharacteristic
256#339C22×C311yescharacteristic
257#339C22×C311yescharacteristic
258#339C22×C311yescharacteristic
259C24×C3—21no—
260C24×C3C2×D412yes—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—21no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8C2×D411yescharacteristic
274C2×C3×D4—21no—
275C2×C3×D4—22no—
276C2×C3×D4—22no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—44no—
289C2×C3×D4—44no—
290C2×C3×D4—82no—
291C2×C3×D4C2×D411yescharacteristic
292C2×C3×D4#4112yes—
293C22×C3×C4—21no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—41no—
302C22×C3×C4—41no—
303C22×C3×C4—82no—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2411yescharacteristic
308C3×SD16—24no—
309C3×D8—24no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—21no—
313C3×M16—21no—
314C3×M16—21no—
315C3×M16—21no—
316C3×M16—21no—
317C3×M16#4112yes—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C3×C4⋊C4—22no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—42no—
337C3×C4⋊C4C2×D411yescharacteristic
338C3×C4⋊C4C2×D411yescharacteristic
339C3×C4⋊C4C2×D411yescharacteristic
340C3×C4⋊C4C2×D411yescharacteristic
341C3×C4⋊C4C2×D411yescharacteristic
342C3×C4⋊C4C2×D411yescharacteristic
343C3×C22⋊C4—22no—
344C3×C22⋊C4—22no—
345C3×C22⋊C4—22no—
346C3×C22⋊C4—22no—
347C3×C22⋊C4—22no—
348C3×C22⋊C4—22no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—22no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—44no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—82no—
362C3×C42—22no—
363C3×C42—22no—
364C3×C42—21no—
365C3×C42—21no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42C2×D411yescharacteristic
374C3×C42C2×D411yescharacteristic
375C3×C42C2×D411yescharacteristic
376C3×C42C2×D411yescharacteristic
377C2×#41C23×C311yescharacteristic
378C22×Q8C23×C311yescharacteristic
379C22×D4—22no—
380C22×D4C23×C311yescharacteristic
381C22×D4C23×C311yescharacteristic
382C23×C4—21no—
383AGL(1,ℤ/8)—22no—
384AGL(1,ℤ/8)—22no—
385C2×SD16—21no—
386C2×D8—21no—
387C2×M16C23×C311yescharacteristic
388C2×M16C23×C311yescharacteristic
389C2×M16C23×C311yescharacteristic
390C2×M16C23×C311yescharacteristic
391C4⋊Q8—21no—
392C4⋊Q8C3×D411yescharacteristic, complemented
393C4⋊Q8C3×D411yescharacteristic, complemented
394#127—21no—
395#127—22no—
396#127—41no—
397#126—22no—
398#126—22no—
399#126—22no—
400#126—22no—
401#125C3×D411yescharacteristic, complemented
402#125C3×D411yescharacteristic, complemented
403#124—22no—
404#124—22no—
405#124—21no—
406#124—21no—
407#124—22no—
408#124—21no—
409#124—21no—
410#124—21no—
411#124—21no—
412#124—41no—
413#123—22no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424#121—21no—
425#121—21no—
426#120—22no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8C3×D411yescharacteristic, complemented
434C4×Q8C3×D411yescharacteristic, complemented
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4C3×D411yescharacteristic, complemented
448C4×D4C3×D411yescharacteristic, complemented
449#117—22no—
450#117—22no—
451#117—22no—
452#117—21no—
453#117C23×C311yescharacteristic
454#117C23×C311yescharacteristic
455#117C23×C311yescharacteristic
456C2×C4⋊C4—21no—
457C2×C4⋊C4C23×C311yescharacteristic
458C2×C22⋊C4—22no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4C3×D412yes—
463C2×C22⋊C4C3×D412yes—
464C2×C42—21no—
465C2×C42C23×C311yescharacteristic
466C2×C42C23×C311yescharacteristic
467C2×C42C23×C311yescharacteristic
468#107—21no—
469#107—21no—
470#107—21no—
471#106—21no—
472#106—21no—
473#106—21no—
474C4⋊C8—21no—
475C4⋊C8—21no—
476#104—41no—
477#104—41no—
478#103—21no—
479#102—21no—
480#102—21no—
481#102—21no—
482#102—21no—
483#102—21no—
484#102—21no—
485#102—21no—
486#101—22no—
487#101—41no—
488#100—22no—
489#100—41no—
490#97—21no—
491C4×C8—21no—
492#95—21no—
493#95—22no—
494C23×C3—22no—
495C23×C3—21no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—42no—
500C23×C3—42no—
501C23×C3—42no—
502C23×C3—42no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3C22×D411yescharacteristic
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—41no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—41no—
512C3×Q8—81no—
513C3×Q8—81no—
514C3×D4—21no—
515C3×D4—22no—
516C3×D4—21no—
517C3×D4—22no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—82no—
527C3×D4—82no—
528C3×D4—88no—
529C2×C3×C4—22no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—22no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—42no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—81no—
552C2×C3×C4—81no—
553C2×C3×C4—82no—
554C2×C3×C4—82no—
555C2×C3×C4—82no—
556C2×C3×C4—82no—
557C2×C3×C4#12011yescharacteristic
558C2×C3×C4#12011yescharacteristic
559C2×C3×C4#12011yescharacteristic
560C2×C3×C4#12011yescharacteristic
561C2×C3×C4C22×D411yescharacteristic
562C2×C3×C4C22×D411yescharacteristic
563C2×C3×C4C2×#4111yescharacteristic
564C2×C3×C4C2×#4111yescharacteristic
565C2×C3×C4H(5,𝔽2)11yescharacteristic
566C2×C3×C42−1+411yescharacteristic
567C3×C8—22no—
568C3×C8—41no—
569C3×C8—41no—
570C3×C8—41no—
571C24—21no—
572C24C2×C3×D412yes—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×C3×D411yescharacteristic
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—82no—
603C2×D4C2×C3×D411yescharacteristic
604C2×D4C3×#4112yes—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—82no—
616C22×C4C2×C3×D412yes—
617C22×C4C2×C3×D411yescharacteristic
618C22×C4C2×C3×D411yescharacteristic
619C22×C4C24×C311yescharacteristic
620SD16—24no—
621D8—24no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16C3×#4112yes—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4C2×C3×D411yescharacteristic
650C4⋊C4C2×C3×D411yescharacteristic
651C4⋊C4C2×C3×D411yescharacteristic
652C4⋊C4C2×C3×D411yescharacteristic
653C4⋊C4C2×C3×D411yescharacteristic
654C4⋊C4C2×C3×D411yescharacteristic
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—82no—
674C42—22no—
675C42—22no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42C2×C3×D411yescharacteristic
686C42C2×C3×D411yescharacteristic
687C42C2×C3×D411yescharacteristic
688C42C2×C3×D411yescharacteristic
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—44no—
692C22×C3—41no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—41no—
696C22×C3—42no—
697C22×C3—41no—
698C22×C3—42no—
699C22×C3—82no—
700C22×C3—82no—
701C22×C3—82no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3C2×#12011yescharacteristic
705C22×C3#54611yescharacteristic
706C22×C3#54711yescharacteristic
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—42no—
712C3×C4—42no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—81no—
721C3×C4—81no—
722C3×C4#52511yescharacteristic
723C3×C4#53711yescharacteristic
724C3×C4#54811yescharacteristic
725C3×C4#55011yescharacteristic
726C23—22no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—41no—
736C23—41no—
737C23C22×C3×D411yescharacteristic
738Q8—21no—
739Q8—21no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—81no—
745Q8—81no—
746D4—21no—
747D4—22no—
748D4—21no—
749D4—22no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—82no—
759D4—82no—
760D4—88no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—82no—
788C2×C4—82no—
789C2×C4C3×#12011yescharacteristic
790C2×C4C3×#12011yescharacteristic
791C2×C4C3×#12011yescharacteristic
792C2×C4C3×#12011yescharacteristic
793C2×C4C22×C3×D411yescharacteristic
794C2×C4C22×C3×D411yescharacteristic
795C2×C4C2×C3×#4111yescharacteristic
796C2×C4C2×C3×#4111yescharacteristic
797C2×C4C3×H(5,𝔽2)11yescharacteristic
798C2×C4C3×2−1+411yescharacteristic
799C8—22no—
800C8—41no—
801C8—41no—
802C8—41no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—81no—
806C2×C3—82no—
807C2×C3—82no—
808C2×C3#240711yescharacteristic
809C2×C3#301811yescharacteristic
810C2×C3#302111yescharacteristic
811C22—21no—
812C22—21no—
813C22—44no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—41no—
820C22—42no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—81no—
825C22—81no—
826C22C2×C3×#12011yescharacteristic
827C22C3×#54611yescharacteristic
828C22C3×#54711yescharacteristic
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—42no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—81no—
843C4—81no—
844C4C3×#52511yescharacteristic
845C4C3×#53711yescharacteristic
846C4C3×#54811yescharacteristic
847C4C3×#55011yescharacteristic
848C3#2414811yescharacteristic, direct product factor, Sylow
849C2—21no—
850C2—21no—
851C2—82no—
852C2—82no—
853C2—81no—
854C2C3×#240711yescharacteristic
855C2C3×#301811yescharacteristic
856C2C3×#302111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2002C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#3510C2semidirect
2. C3×#3077C2semidirect
3. C3×C4×AGL(1,ℤ/8)C2semidirect
4. C3×#2544C2semidirect
5. C3×#2038C2semidirect
6. C3×#2037C2semidirect
7. C3×#2003C2semidirect
9. C3×#1986C2semidirect
10. C3×#1967C2semidirect
11. C3×#1888C2semidirect
12. C3×#1887C2semidirect
13. C3×#1857C2semidirect
14. C3×#1856C2semidirect
15. C3×#1806C2semidirect
16. #24148C3direct (N × H)
72. #3510C2×C3semidirect
73. #3077C2×C3semidirect
74. C4×AGL(1,ℤ/8)C2×C3semidirect
75. #2544C2×C3semidirect
76. #2038C2×C3semidirect
77. #2037C2×C3semidirect
78. #2003C2×C3semidirect
80. #1986C2×C3semidirect
81. #1967C2×C3semidirect
82. #1888C2×C3semidirect
83. #1887C2×C3semidirect
84. #1857C2×C3semidirect
85. #1856C2×C3semidirect
86. #1806C2×C3semidirect
102. C3×C4⋊Q8D4semidirect
103. C3×C4⋊Q8D4semidirect
111. C3×#125D4semidirect
112. C3×#125D4semidirect
143. C3×C4×Q8D4semidirect
144. C3×C4×Q8D4semidirect
157. C3×C4×D4D4semidirect
158. C3×C4×D4D4semidirect
392. C4⋊Q8C3×D4semidirect
393. C4⋊Q8C3×D4semidirect
401. #125C3×D4semidirect
402. #125C3×D4semidirect
433. C4×Q8C3×D4semidirect
434. C4×Q8C3×D4semidirect
447. C4×D4C3×D4semidirect
448. C4×D4C3×D4semidirect
848. C3#24148direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#35102
C3×#30772
C3×C4×AGL(1,ℤ/8)2
C3×#25442
C3×#20382
C3×#20372
C3×#20032
C3×#20022
C3×#19862
C3×#19672
C3×#18882
C3×#18872
C3×#18572
C3×#18562
C3×#18062
#241483